Theory of Probability &Its Applications, Volume 66, Issue 1, Page 105-120, January 2021.
We consider a communication network with a fixed set of links that are shared by a large number of users. The resource allocation is performed on the basis of the aggregate utility maximization in accordance with the popular approach proposed by F. Kelly and coauthors in 1998. The problem is to construct a pricing mechanism for transmission rates in order to stimulate an optimal allocation of the available resources. In contrast to the usual approach, the proposed algorithm does not use the information on the aggregate traffic over each link. This algorithm's inputs are the total number $N$ of users, the link capacities, and optimal myopic reactions of randomly selected users to the current prices. The dynamic pricing scheme is based on the dual stochastic gradient projection method. For a special class of utility functions $u_i$, we obtain upper bounds for the constraint residuals and for the deviation of the objective function from the optimal value. These estimates are uniform in $N$ and of order $O(T^{-1/4})$ in the number $T$ of measured user reactions. We present the results of computer experiments for quadratic functions $u_i$, which are the differences between the linear utilities, which are individual for each user, and the quadratic penalty assigned by the network.

中文翻译：

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大量用户通信网络中的资源分配：双随机梯度法

概率论及其应用，第 66 卷，第 1 期，第 105-120 页，2021 年 1 月。
我们考虑具有一组固定链接的通信网络，这些链接由大量用户共享。根据 F. Kelly 和合著者在 1998 年提出的流行方法，在总效用最大化的基础上进行资源分配。 问题是构建传输速率的定价机制，以刺激可用资源的优化分配。资源。与通常的方法相反，所提出的算法不使用关于每个链路上的聚合流量的信息。该算法的输入是用户总数 $N$、链接容量以及随机选择的用户对当前价格的最佳近视反应。动态定价方案基于双随机梯度投影方法。对于一类特殊的效用函数 $u_i$，我们获得约束残差和目标函数与最佳值的偏差的上限。这些估计在 $N$ 和 $O(T^{-1/4})$ 数量级上是一致的，在测量的用户反应数量 $T$ 中。我们展示了二次函数 $u_i$ 的计算机实验结果，这是线性效用之间的差异，对于每个用户来说都是个体的，与网络分配的二次惩罚之间的差异。